Skip to main content
Log in

Intersecting subvarieties of abelian varieties with algebraic subgroups of complementary dimension

  • Published:
Inventiones mathematicae Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Ax, J.: Some topics in differential algebraic geometry I: Analytic subgroups of algebraic groups. Am. J. Math. 94, 1195–1204 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bombieri, E., Gubler, W.: Heights in Diophantine Geometry. Cambridge University Press, Cambridge (2006)

    MATH  Google Scholar 

  3. Bombieri, E., Masser, D., Zannier, U.: Intersecting a curve with algebraic subgroups of multiplicative groups. Int. Math. Res. Not. 20, 1119–1140 (1999)

    Article  MathSciNet  Google Scholar 

  4. Bombieri, E., Masser, D., Zannier, U.: Anomalous subvarieties – structure theorems and applications. Int. Math. Res. Not. 19, 1–33 (2007)

    Google Scholar 

  5. Bombieri, E., Masser, D., Zannier, U.: Intersecting a plane with algebraic subgroups of multiplicative groups. Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 7, 51–80 (2008)

    MATH  MathSciNet  Google Scholar 

  6. Bombieri, E., Masser, D., Zannier, U.: On unlikely intersections of complex varieties with tori. Acta Arith. (to appear)

  7. Carrizosa, M.: Problème de Lehmer et variétés abéliennes CM. C. R. Acad. Sci., Paris, Sér. I (2008). Doi:10.1016/j.crma.2008.10.004

  8. Carrizosa, M.: Problème de Lehmer relatif pour les variétés abéliennes CM. Ph.D. thesis, Université Paris 6 (2008)

  9. Cassels, J.W.S.: An Introduction to Diophantine Approximation. Cambridge University Press, Cambridge (1965)

    Google Scholar 

  10. Danilov, V.I.: Algebraic varieties and schemes. In: Shafarevich, I.R. (ed.) Algebraic Geometry I, Encycl. Math. Sci., vol. 23. Springer, Berlin (1994)

  11. Fulton, W.: Intersection Theory. Springer, Berlin (1984)

    MATH  Google Scholar 

  12. Grauert, H., Remmert, R.: Coherent Analytic Sheaves. Springer, Berlin (1984)

    MATH  Google Scholar 

  13. Habegger, P.: On the bounded height conjecture. Int. Math. Res. Not. (to appear)

  14. Lang, S.: Fundamentals of Differential Geometry. Springer, New York (2001)

    MATH  Google Scholar 

  15. Lazarsfeld, R.: Positivity in Algebraic Geometry I. Springer, Berlin (2004)

    Google Scholar 

  16. Mumford, D.: Abelian Varieties. Oxford University Press, London (1970)

    MATH  Google Scholar 

  17. Pink, R.: A common generalization of the conjectures of André–Oort, Manin–Mumford, and Mordell–Lang. Preprint

  18. Ratazzi, N.: Intersection de courbes et de sous-groupes et problèmes de minoration de hauteur dans les variétés abéliennes C.M. Ann. Inst. Fourier 58(5), 1575–1633 (2008)

    MATH  MathSciNet  Google Scholar 

  19. Rémond, G.: Intersection de sous-groupes et de sous-variétés I. Math. Ann. 333, 525–548 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  20. Rémond, G.: Intersection de sous-groupes et de sous-variétés II. J. Inst. Math. Jussieu 6(2), 317–348 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  21. Rémond, G.: Intersection de sous-groupes et de sous-variétés III. Comment. Math. Helv. (to appear)

  22. Schinzel, A.: Polynomials with Special Regard to Reducibility. With an Appendix by Umberto Zannier. Encycl. Math. Appl., vol. 77. Cambridge University Press, Cambridge (2000)

    Google Scholar 

  23. Viada, E.: The intersection of a curve with algebraic subgroups in a product of elliptic curves. Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 2, 47–75 (2003)

    MATH  MathSciNet  Google Scholar 

  24. Weyl, H.: The Classical Groups. Their Invariants and Representations. Princeton University Press, Princeton, NJ (1973)

    Google Scholar 

  25. Whitney, H.: Complex Analytic Varieties. Addison-Wesley, Reading, MA (1972)

    MATH  Google Scholar 

  26. Zannier, U.: Appendix by Umberto Zannier in [22], pp. 517–539 (2000)

  27. Zilber, B.: Exponential sums equations and the Schanuel conjecture. J. Lond. Math. Soc., II. Ser. 65(1), 27–44 (2002)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to P. Habegger.

Additional information

Mathematics Subject Classification (2000)

11G50 (primary), 14K15, 14G40, 14J20

Rights and permissions

Reprints and permissions

About this article

Cite this article

Habegger, P. Intersecting subvarieties of abelian varieties with algebraic subgroups of complementary dimension. Invent. math. 176, 405–447 (2009). https://doi.org/10.1007/s00222-008-0170-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00222-008-0170-6

Keywords

Navigation